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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 58800.fh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.fh1 | 58800kg2 | \([0, 1, 0, -274808, -58759212]\) | \(-7620530425/526848\) | \(-158676839301120000\) | \([]\) | \(746496\) | \(2.0514\) | |
58800.fh2 | 58800kg1 | \([0, 1, 0, 19192, -76812]\) | \(2595575/1512\) | \(-455386337280000\) | \([]\) | \(248832\) | \(1.5021\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.fh have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.fh do not have complex multiplication.Modular form 58800.2.a.fh
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.